class summaries: March 30

calc III: lines and planes.

topology: homotopy invariance of homology.

class summaries: March 28

calc III: cross products. long live torque!

topology: the homology of a point, the 0-th homology group. algebra rules!

class summaries: March 26

calc III: vectors and dot products.

topology: introduced singular homology.

class summaries: March 23

calc III: 3-d coordinate systems; handed back tests.

topology: finished the proof of the Poincare-Hopf Theorem. next up: singular homology!

class summaries: March 21

calc III: test.

topology: more of the proof of the Poincare-Hopf theorem. will finish this next time.

class summaries: March 19

well, spring break is over and it's back to the grind.

Calc III: review for test #2. remember, it's on Wednesday, March 21.

Topology: trying to prove the Poincare-Hopf Theorem. lots of technicalities. nondegenerate zeros are better, so we'll try to reduce to that.

class summaries: March 7

calculus III: areas and lengths of polar curves. the cardioid has length 8(!).

topology: the index of a vector field on a manifold.

class summaries: March 5

calculus III: polar graphs, etc. almost done with chapter 11!

topology: tangent vector fields on manifolds; there's a nowhere-vanishing vector field on the n-sphere if and only if n is odd.

Colbert on topology

Let's start a petition for Colbert to win the Fields Medal at the 2010 ICM!

Click here.

class summaries: March 2

calculus III: introduced polar coordinates. graphed some stuff.

topology: proved that the Brouwer degree is a smooth homotopy invariant.

class summaries: February 28

calculus III: lengths of parametrized curves; surface area of solids of revolution

topology: more about oriented manifolds; Brouwer degree